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Chapter 1  Limits, Alternatives, Choices Worked Problems
1. Consider that you have an income of $80 a week.
You decide to purchase two goods:
tacos and movie tickets.
Tacos (yvariable) cost $1 and movie tickets (xvariable) cost
$8.
a) What is the slope of the budget line assuming you exhaust your income?
b) What is the opportunity cost of consuming one more movie ticket? One more taco?
c) Now, suppose that your that you found $16 on the ground; what happens to your
budget constraint?
Graph this.
What is the slope of the budget constraint now?
a)
80 1
8
t
mt
M
PT
P MT
T
MT
=
+
⇒
=
+
Setting one good equal to zero and repeat.
T = 80
and MT = 10.
b) The opportunity cost of 1 more movie ticket is 8 tacos, and the opportunity cost of one
more taco is 1/8 of a movie ticket.
c) If you find $16 on the ground, then your income increases from $80 to $96.
As a
result, your budget constraint shifts outwards parallel to the original budget constraint.
The slope still remains 8, as the line was shifted not rotated.
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Assume that a consumer has $12 in income and she can buy only two goods, apples
or bananas. The price of an apple is $1.50 and the price of a banana is $0.75.
a. If the consumer spent all of her money on either apples or bananas, how many apples
or how many bananas would she be able to buy?
b. What is the slope of the budget line for apples and bananas if apples were graphed on
the horizontal axis and bananas were graphed on the vertical axis?
c. If the consumer decides to buy 4 apples, how many bananas can she also buy with the
rest of her income?
d. For this consumer, the opportunity cost of buying another apple is
a)
8 apples or 16 bananas.
If you set bananas equal to 0 you have $12 = $1.50*A.
Divide through to get 8 apples.
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 Spring '09
 Slope, Limits

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